Geometry Projects

The boys have put themselves in the role of a Creator. They were given the assignment to create their dream club house, play house, or hunting blind. They could build it from things around their house, Sketch-Up, or legos. We have been talking about how Geometry is all around us. I wanted to end this unit with them taking on a role where they could experience hands on Geometry. I will be showing you their projects soon.

"I used to think, but now I think" --- Geometry

I asked the boys to type or write out a "I used to think, but now I think" on Geometry. I wanted to share a few with you.




I use to think Geometry was just shapes and sides. Now I think Geometry it more complex than J.K. Rowling's writing style.

I use to think Geometry was just a bunch of shapes. Now I think it is mathematical term like multiplication or division.

I used to think Geometry was useless. Now I think Geometry is in our everyday life.

I use to think Geometry was just a bunch of Shapes. Now I think Geometry is something we use everyday.

I use to think that Geometry does not involve anything in real life. Now I think that you can find Geometry everywhere.

Geometry Unit

I am so excited about what has come out of this unit. I will continue to teach Geometry this way in the future. The boys have really immersed themselves in geometry and want to learn more. They could not believe that we have only touched the surface of what geometry is all about. They keep wanting to learn more. The classes were run by what questions the boys wanted to learn about and the tests were based on their questions.

As we got into the unit and started to learn about the formulas the boys were able to figure out some of the formulas because of the definitions that they have learned. For example, I had them figure out the area of a triangle on their own. They knew that a triangle was half of a parallelogram and the formula for a parallelogram was base x height. Knowing this information they were able to come up with the formula for a triangle and explain why. ((base x height)/2) This was exciting for them. They also figured out that circumference has two different formulas and can explain why. They knew that a diameter was made up of two radii.

The boys also started to ask questions about volume and why the formula changed depending on the bases of the 3D object. When we got into these questions the boys realized that you can write volume as Area of the base x Height of the whole object. This then lead into what happens if you have something inside the 3D object taking up space in the object.

This lead to the questions, "What does a 4D shape look like?" and "Do they exist?" These question lead into some great debates. The boy continue to research and ask questions.

Random Guy

We have brought Random guy back into the classroom. The boys are now teaching him about geometry. The boys are having so much fun with Random Guy. Over the year, the boys have found this exercise is a great way to check their work. I would love to share some of their Random Guy writings with you. As they write to Random Guy they are told to write their thoughts and not worry about all the grammar. I feel that if they are not as concerned about their grammar, their explanations will be more complete.

I have provided some examples below. In some of the examples the boys left out why they had to subtract. We talked about why that was important to put into to the explanation. I am very proud of the boys for what they came up with. This was given to them with only one measurement and they had to find out the other measurements and the formulas. Not all of the following examples are perfect scores. I wanted to show different examples of the progress the boys are making. I have discovered during this process that the boys are better able to see their errors and I am better able to assess their needs so that they can fully understand what they are doing.

In some of the following examples the boys and I talked about how some of the details were left out. For Example, "Why subtract the area of the circle from the area of the square?" or "How did you get 8 units as the length of one side of the square?" I feel the boys are doing a great job. The boys that wrote this knew the answers to the questions I asked, he just forgot to put it into the explanation. This is another great learning tool. The boys are able to use peer editing and teaching each other at the same time.

Here is the question that the following boys wrote about.

Area and Perimeter

Today we talked about area and perimeter of a parallelogram. We talked about the formulas, how you label the units and when we can use area and perimeter in everyday life.

Area = base x height
Perimeter = You just always add up all the sides.

One of the questions in class was, Why do you square the units when finding area and do nothing to the units when finding perimeter?

Some of the boys talked about how you are multiplying like units together and that is why you square them in area. You add in perimeter so you do not need to do anything to the units in perimeter.

One boy made a connection to a two dimensional plane and squaring the units in area. He talked about how a plane is two dimension and you only have length and a width, or a base and a height. You have no depth. Therefore, you need to square your units. You have two units you are multiplying together. Then he talked about how perimeter means you are going around a plane. Lines make up planes and lines are one dimension. Therefore you do not need to do anything with the units. The boys really liked that way of looking at area and perimeter.

Making Connections

This has been an amazing few weeks for me as a teacher. As I talked about earlier, I decided to teach my Geometry unit differently this year. I first had the boys set up a slide show from their research of different Geometry words that I had given them. Then I set the class up as a discussion, debate, and investigation format. I could have never dreamed about how well it went. The boys came up with amazing questions and connections. They had to back up everything with proof. I cannot wait to hear what they come up with next. We are going to be starting to add in some formulas into the discussions.

I would love to hear about different ways your school is teaching geometry.

Geometry Vocab Discussion Cont.

Here are some examples of questions that came from our class discussions this week.
1. Does every polygon with equal angles, have equal sides? -- This question came up when we were talking about equilateral triangles. After the boy asked the question, another boy raised his hand and said, "No". I said, "Why?" He said, "A rectangle has equal angles, but not equal sides."

2. What can you call a diagonal in a square that cuts the 90 degree angles in half?

3. Question two lead into the discovery that two right triangles make up a square. Also that the sum of all the angles in a triangle is 180 degrees and 180 degrees + 180 degrees = 360 degrees. 360 degrees is the sum of all the angles in a quadrilateral.

4. Are all angles that make up complementary angles acute? -- We used the definition of complementary angles and acute angles to come up with our answer.

5. Do all right triangles have complementary angles? --- They boys used the definition of a right triangle, the definition of complementary angles, and that the sum of all the angles in a triangle is 180 degrees.

6. Do 4 radii make up a circumference?

7. Do 6 radii make up a circumference?

--- To solve questions 6 and 7 we had to look at what circumference equaled.

8. Why do you call 22/7 Pi?

10. Could a diameter also be called a line of symmetry? -- This question came up when we were talking about what cuts a circle in half. One of the boys said a line of symmetry. We talked about how a diameter is like a line of symmetry in a circle. I loved how he made the connection.

*** The boys discovered on their own that if C=(pi)d, then circumference also equals two times Pi times radius. They were very proud of themselves for discovering this formula.


Similes:
The earth's core is like the diameter in a circle, because they both go straight though the center connecting each side.

Geometry Discussion

For the last few days we have been talking about geometry and how it is all around us. The boys were given words they were required to research on their own and then teach their words to the class. We used Google Docs to put the slide show together. I asked the boys, "How does Geometry shape our world?" The discussions we have been getting into are amazing. The boys have really been digging deep into the vocab and seeing how it relates to the world around us.
1. Where are rays represented in our world?

Is a piece of hair a ray?

Are your fingernails rays?
We have decided with a lot of discussion that both these things are rays. The boys supported this answer by explaining how your hair starts at the scalp like the end of a ray and your hair can grow forever on the other end like the other end of a ray. The same thing happens with your figure nails. One end can go on forever and the other has a stopping point.

2. Are points considered a zero dimension if points make up lines and lines are one dimension?
When we talk about the definition of a point it talks about a point having no depth and no length. Therefore we concluded that a point does not have a dimension. A point does have a zero dimension.

3. Is a circle a plane and made up of lots of little lines?
I left the boys with a question to think about over the weekend. I asked them, "Can you prove that circles are polygons?"

Similes of The Week:
An angle is like two or more jets moving into a formation or peeling away from each other. vertex is the point where they start before pealing out.

Intersecting lines and parallel lines are like fraternal twins. They are in the same family, but have different characteristics.

A point is like the Holy Spirit you know they both exist, but you cannot see them.